Question: Simplify the following expression: $r = \dfrac{p^2 - 9p - 10}{p - 10} $
First factor the polynomial in the numerator. $ p^2 - 9p - 10 = (p - 10)(p + 1) $ So we can rewrite the expression as: $r = \dfrac{(p - 10)(p + 1)}{p - 10} $ We can divide the numerator and denominator by $(p - 10)$ on condition that $p \neq 10$ Therefore $r = p + 1; p \neq 10$